I stumbled upon this which looks like a promising way of implementing an orientation test.
I'm not interested in the described adaptive approach, I'm fine with using the naive determinant approach by checking if it evaluates to greater/less/equal 0. As I understand it, the only difference is that the more sophisticated adaptive approach will always work (won't suffer from round-off errors do to floating point arithmetic) whereas the naive determinant approach occasionally fails due to round-off errors. Is this correct?
I'm wondering if there are any easy to implement alternatives to the determinant approach? That is, if someone asked you to implement the orientation test without using the determinant approach, what would you do?